Measure ω , c -Pseudo-Almost Periodic Functions and Lasota-Wazewska Model with Ergodic and Unbounded Oscillating Oxygen Demand

Most of the natural phenomena we consider as periodic are in fact almost periodic; in other words, they are periodic up to epsilon. The concept of almost periodic functions was introduced in the literature in the mid-1920s by the Danish mathematician Harald Bohr [1]. It was later generalized in various directions by many researchers [2–12]. As we all know, many phenomena in nature have oscillatory character, and their mathematical models have led to the introduction of certain classes of functions to describe them. Such a class form pseudo-almost periodic functions which is a natural generalization of the concept of almost periodicity (in Bohr’s sense). In this work, we introduce the notion of measure -pseudo-almost periodic functions (or --pseudo-almost periodic functions) with values in a complex Banach space and enlighten their applications throughout the study of a biological model. This work generalizes the concept of -pseudo-almost periodic functions introduced by Blot et al. [4] which already generalizes the class of weighted pseudo-almost periodic functions of Diagana [6, 13]. Here, we investigate many interesting properties of this new class of functions and present new and more general results based on measure theory that extend the existing ones.